scholarly journals Exploring the effects of missing data on the estimation of fractal and multifractal parameters based on bootstrap method

2018 ◽  
Author(s):  
Xin Gao ◽  
Xuan Wang
Keyword(s):  
Time Series ◽  
Statistical Inference ◽  
Missing Values ◽  
Interpolation Method ◽  
Piecewise Linear ◽  
Bootstrap Method ◽  
Linear Interpolation ◽  
Estimation Accuracy ◽  
Bootstrap Resampling ◽  
Piecewise Linear Interpolation

Abstract. A time series collected in the nature is often incomplete or contains some missing values, and statistical inference on the population or process with missing values, especially the population or process having multifractal properties is easy to ignore. In this study, the simulation and actual data were used to obtain the probability distributions of fractal parameters through a new bootstrap resampling mechanism with the aim to statistically infer the estimation accuracy of the time series containing missing values and four kinds of interpolated series. Firstly, the RMS errors results showed that compared with the four interpolation methods for one parameter H required for fBm the direct use of the series with missing values has the highest estimation accuracy, while it shows certain instability in the estimations of the multifractal parameters C1 and α, especially at higher missing levels, however, the accuracy of the parameters estimated by preprocessing of piecewise linear interpolation method can be improved; in addition, it is also concluded that α is more sensitive to the changes caused by these processing than another parameter C1. Secondly, the effects on the ability of statistical inference for a population caused from the data losses are explored through the estimation of confidence intervals and hypothesis testing by proposing a new bootstrap resampling mechanism, and the conclusions showed that whether it is a mono-fractal parameter or multifractal parameters, the large deviations from the estimates of original series occur on the series with missing values when the losses are serious, while the defects can be compensated by the preprocessing using PLI and PBI methods; similarly, although the results of the incomplete series at the low missing levels are close to the original and PLI series, while at the high missing levels, the probabilities of Type II Errors of the neighboring values are unable to ignore, but the PLI or PBI method can avoid the erroneous judgments.

A Safe Flight Approach of the UAV in the Electrical Line Inspection

2015 ◽  
Vol 16 (5) ◽  
pp. 503-515 ◽  
Author(s):  
Changan Liu ◽  
Yang Liu ◽  
Hua Wu ◽  
Ruifang Dong
Keyword(s):  
Distribution Curve ◽  
Interpolation Method ◽  
Piecewise Linear ◽  
Linear Interpolation ◽  
Flight Path ◽  
Artificial Potential Field ◽  
Piecewise Linear Interpolation ◽  
Vehicle Inspection ◽  
Aerial Vehicle ◽  
Low Costs

Abstract In recent years, the UAV (Unmanned Aerial Vehicle) inspection for the electrical line has received increasing attentions due to the advantages of low costs, easiness to control and flexibility. The UAV can inspect the electrical tower independently and automatically by planning the flight path. But during the inspection along the path, the UAV is easily impacted by gust wind due to its light weight and small size, which always leads to the crash into the electrical tower. Thus, in this paper, a safe flight approach (SFA) is proposed to make the flight be safer during the inspection. The main contributions include: firstly, the piecewise linear interpolation method is proposed to fit the distribution curve of the electrical towers based on the GPS coordinates of the electrical towers; secondly, the no-fly zone on the both sides of the distribution curve are created, and a security distance formula (SDF) is raised to decide the width of the no-fly zone; thirdly, a gust wind formula (GWF) is proposed to improve the artificial potential field approach, which can contribute to the path planning of the UAV; finally, a flight path of the UAV can be planned using the SFA to make the UAV avoid colliding with the electric tower. The proposed approach is tested on the experiment to demonstrate its effectiveness.

scholarly journals Interp-SUM: Unsupervised Video Summarization with Piecewise Linear Interpolation

Sensors ◽  
2021 ◽  
Vol 21 (13) ◽  
pp. 4562
Author(s):  
Ui-Nyoung Yoon ◽  
Myung-Duk Hong ◽  
Geun-Sik Jo
Keyword(s):  
Large Scale ◽  
Interpolation Method ◽  
Piecewise Linear ◽  
Video Summarization ◽  
Linear Interpolation ◽  
The State ◽  
Experimental Result ◽  
Natural Sequence ◽  
Reward Function ◽  
Piecewise Linear Interpolation

This paper addresses the problem of unsupervised video summarization. Video summarization helps people browse large-scale videos easily with a summary from the selected frames of the video. In this paper, we propose an unsupervised video summarization method with piecewise linear interpolation (Interp-SUM). Our method aims to improve summarization performance and generate a natural sequence of keyframes with predicting importance scores of each frame utilizing the interpolation method. To train the video summarization network, we exploit a reinforcement learning-based framework with an explicit reward function. We employ the objective function of the exploring under-appreciated reward method for training efficiently. In addition, we present a modified reconstruction loss to promote the representativeness of the summary. We evaluate the proposed method on two datasets, SumMe and TVSum. The experimental result showed that Interp-SUM generates the most natural sequence of summary frames than any other the state-of-the-art methods. In addition, Interp-SUM still showed comparable performance with the state-of-art research on unsupervised video summarization methods, which is shown and analyzed in the experiments of this paper.

Comparison of two gap-filling techniques for nitrous oxide fluxes from agricultural soil

2019 ◽  
Vol 99 (1) ◽  
pp. 12-24 ◽  
Author(s):  
Rezvan Taki ◽  
Claudia Wagner-Riddle ◽  
Gary Parkin ◽  
Rob Gordon ◽  
Andrew VanderZaag
Keyword(s):  
Missing Values ◽  
Interpolation Method ◽  
Weather Conditions ◽  
Linear Interpolation ◽  
Bias Error ◽  
Research Station ◽  
Ann Model ◽  
Gap Filling ◽  
Adverse Weather ◽  
The Impact

Micrometeorological methods are ideally suited for continuous measurements of N2O fluxes, but gaps in the time series occur due to low-turbulence conditions, power failures, and adverse weather conditions. Two gap-filling methods including linear interpolation and artificial neural networks (ANN) were utilized to reconstruct missing N2O flux data from a corn–soybean–wheat rotation and evaluate the impact on annual N2O emissions from 2001 to 2006 at the Elora Research Station, ON, Canada. The single-year ANN method is recommended because this method captured flux variability better than the linear interpolation method (average R2 of 0.41 vs. 0.34). Annual N2O emission and annual bias resulting from linear and single-year ANN were compatible with each other when there were few and short gaps (i.e., percentage of missing values <30%). However, with longer gaps (>20 d), the bias error in annual fluxes varied between 0.082 and 0.344 kg N2O-N ha−1 for linear and 0.069 and 0.109 kg N2O-N ha−1 for single-year ANN. Hence, the single-year ANN with lower annual bias and stable approach over various years is recommended, if the appropriate driving inputs (i.e., soil temperature, soil water content, precipitation, N mineral content, and snow depth) needed for the ANN model are available.

scholarly journals Crank-Nicolson scheme for two-dimensional in space fractional diffusion equations with functional delay

2021 ◽  
Vol 57 ◽  
pp. 128-141
Author(s):  
M. Ibrahim ◽  
V.G. Pimenov
Keyword(s):  
Piecewise Linear ◽  
Linear Interpolation ◽  
Fractional Diffusion ◽  
Dimensional System ◽  
Two Dimensional ◽  
Piecewise Linear Interpolation ◽  
Functional Delay ◽  
General Difference ◽  
Nicolson Scheme ◽  
Crank Nicolson

A two-dimensional in space fractional diffusion equation with functional delay of a general form is considered. For this problem, the Crank-Nicolson method is constructed, based on shifted Grunwald-Letnikov formulas for approximating fractional derivatives with respect to each spatial variable and using piecewise linear interpolation of discrete history with continuation extrapolation to take into account the delay effect. The Douglas scheme is used to reduce the emerging high-dimensional system to tridiagonal systems. The residual of the method is investigated. To obtain the order of the method, we reduce the systems to constructions of the general difference scheme with heredity. A theorem on the second order of convergence of the method in time and space steps is proved. The results of numerical experiments are presented.

Median based algorithm for sub-pixel estimation of extrema positions of diffuse light reflection signal

2021 ◽  
Vol 2021 (49) ◽  
pp. 37-44
Author(s):  
I. B. Ivasiv ◽  
Keyword(s):  
Linear Array ◽  
Piecewise Linear ◽  
Linear Interpolation ◽  
Diffuse Light ◽  
Random Errors ◽  
Centroid Algorithm ◽  
Piecewise Linear Interpolation ◽  
Light Reflectance ◽  
Cumulative Function

It has been proposed to utilize the median algorithm for determination of the extrema positions of diffuse light reflectance intensity distribution by a discrete signal of a photodiode linear array. The algorithm formula has been deduced on the base of piecewise-linear interpolation for signal representation by cumulative function. It has been shown that this formula is much simpler for implementation than known centroid algorithm and the noise immune Blais and Rioux detector algorithm. Also, the methodical systematic errors for zero noise as well as the random errors for full common mode additive noises and uncorrelated noises have been estimated and compared for mentioned algorithms. In these terms, the proposed median algorithm is proportionate to Blais and Rioux algorithm and considerably better then centroid algorithm.

scholarly journals Treatment of Outlier Using Interpolation Method in Malaysia Tourist Arrivals

2018 ◽  
Vol 7 (3.7) ◽  
pp. 51
Author(s):  
Maria Elena Nor ◽  
Norsoraya Azurin Wahir ◽  
G P. Khuneswari ◽  
Mohd Saifullah Rusiman
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
Performance Indicator ◽  
Interpolation Method ◽  
Spline Interpolation ◽  
Forecast Accuracy ◽  
Linear Interpolation ◽  
Negative Influence ◽  
Series Data ◽  
Missing Value

The presence of outliers is an example of aberrant data that can have huge negative influence on statistical method under the assumption of normality and it affects the estimation. This paper introduces an alternative method as outlier treatment in time series which is interpolation. It compares two interpolation methods using performance indicator. Assuming outlier as a missing value in the data allows the application of the interpolation method to interpolate the missing value, thus comparing the result using the forecast accuracy. The monthly time series data from January 1998 until December 2015 of Malaysia Tourist Arrivals were used to deal with outliers. The results found that the cubic spline interpolation method gave the best result than the linear interpolation and the improved time series data indicated better performance in forecasting rather than the original time series data of Box-Jenkins model. 

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